While 49 states have concealed carry laws on their books, many are "may issue" states vs. "shall issue" states. "May issue" states can deny a citizen a permit for any number of arbitrary reasons as the state has no legal obligation to issue a permit. "Shall issue" states must issue a permit if an application is filed unless the applicant is barred from owning firearm under federal law.
20 states along with the CATO and others have filed Amici Curiae (friends of the court) briefs to urge the Supreme Court of the United States hear Mr. Gura's lawsuit (Kachalsky, et al v. Cacase, et al). The NRA and the Firearms Policy Coalition also filed briefs, however it is thought that the 20 states coming on board may be enough to have the case heard by the SCOTUS.
The importance of winning this case at the SCOTUS level can not be over stated. A favorable ruling would force May Issue states such as NY and California to issue permits to all citizens who file applications that are legally able to own a firearm.
Here are links to the briefs that have been filed thus far.
American Civil Rights Union
Center for Constitutional Jurisprudence
Academics for the Second Amendment
SCOPE, NJ2AS, Comm2A, LSAPA